Possession seems to be perma-banned (and for good reason), but one of them showed up in my Black Market deck in a game I played a week or two ago. Unfortunately I didn't write down the game number. I have not seen Stash appear in black market decks, at least.

Stash is simply not implemented, so it cannot appear at all. Possession is 'just' on the list of banned cards for filling a kingdom with random cards. That Possession can appear in Black Market has been remarked from time to time.

I *think* the argument is that Possession in the kingdom can lead to games where both players have more turns when they are possessed than normal ones and that makes the game go the route of "Make your own deck as bad as possible". A single Possession in the Black Market deck is obviously a very potent card, but that is the nature of Black Market: One player may get an effect that is otherwise not represented on the board.